Semiconductor material characterizing method and apparatus

ABSTRACT

A method and apparatus are provided for determining the doping concentration profile of a specimen of semiconductor material. The apparatus includes a sensor assembly having a sensor tip which is mounted on an air bearing assembly. The air bearing assembly is suspended from a housing by a pair of bellows. In use, air is supplied to the air bearing assembly through the bellows causing the bellows to expand, lowering the sensor tip until the air bearing action stops the expansion. In other implementations of the invention, photocurrent or photovoltage are not used and the doping concentration profile is determined using the total capacitance, the capacitance of air, the DC bias voltage and the area of the electrode spaced from the specimen information.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method and apparatus forcharacterizing a specimen of semiconductor material and, moreparticularly, to a method and apparatus determining parameters such asthe doping concentration profile of a specimen of semiconductormaterial.

2. Description of Prior Art

Various methods for measurements of semiconductor surface andsemiconductor/insulator interface parameters have been described. Theycan be classified into destructive and non-destructive. Examples ofdestructive methods are the secondary ion mass spectrometry and thefour-point sensor method.

Non-destructive methods can be further classified into those requiringpost-processing and those that don't (post-processing is defined asadditional processing steps beyond those that define properties ofsemiconductor surface or semiconductor/insulator interface that are thegoal of characterization). An example of a method that requirespost-processing are traditional Metal-Insulator-Semiconductor Volt-Farad(MIS CV) measurements. They require presence of an insulator over thesemiconductor surface and deposition of a metal layer over theinsulator. Additional steps are costly, time-consuming and they canchange the properties that were the goal of measurements.

Methods that do not require post-processing can be subdivided intocontact and non-contact methods. Contact methods are defined as thosethat involve bringing the specimen into physical contact with materialsor chemicals other than the ambient environment or materials andequipment that are used to handle specimens (semiconductor wafers)during normal processing steps, such as cleaning, annealing,implantation, etc. Since such methods require direct contact of aforeign material with the front side of the wafer there is a risk ofcontaminating the wafer, therefore they are not used with productionwafers.

Finally, several non-contact methods for semiconductor surface/interfacecharacterization are known in the field.

The apparatus described in U.S. Pat. No. 5,233,291 uses traditional CVmethodology for measurement of the properties of semiconductor surfaceand semiconductor/insulator interface. The difference between theapparatus in U.S. Pat. No. 5,233,291 and MIS CV measurement systems isin the use of precisely controlled air gap as the insulating layerbetween the metal electrode and the semiconductor. Wafer proximity isdetermined by detecting the energy losses of the laser beam thatundergoes total internal reflection on the surface of the transparentconductive electrode caused by interaction of the sample with theevanescent beam. The electrode is suspended at submicron distance fromthe sample, this distance as well as tip and tilt being monitored bythree capacitive sensors and controlled by three piezo actuators in realtime during the measurements.

In order to calculate semiconductor parameters using CV methods, it isnecessary to know the width of the depletion layer in the semiconductor.W_(d). In the method in U.S. Pat. No. 5,233,281, W_(d) is calculatedfrom the capacitance of the depletion layer, which in turn is calculatedfrom the total capacitance between the metal electrode and thesemiconductor substrate.

    C.sub.tot.sup.-1 =C.sub.air.sup.-1 +C.sub.SiO2.sup.-1 +C.sub.Si.sup.-1,

Thus, it is important to know C_(air) ⁻¹ +C_(SiO2) ⁻¹ at all timesduring the measurement, which means either measuring the air gap,holding it fixed with substantial precision during the measurements ofelectrical parameters of the sample, or being able to calculate it atall times during the measurement based on previously characterizing thebehavior of the air gap.

Additionally, the method described in U.S. Pat. No. 5,233,291 is notwell suited for measurements of samples with poorly passivatedsemiconductor/insulator interface, e.g. non-passivated wafers ofepitaxially grown films, because of the presence of slow surface stateswhich may recharge during the measurements and thus affect both themeasurements of C_(Si) ⁻¹.

The surface photovoltage method described in U.S. Pat. No. 4,827,212 toE. Kamienicki, which patent is incorporated herein by reference, makesuse of modulated light whose wavelength corresponds to an energy greaterthan the band gap of the semiconductor and whose modulation frequency isgreater than the reciprocal lifetime of minority carriers and whoseintensity is low enough so that the modulation of the semiconductorsurface potential is small compared to the surface potential. Thephotovoltage generated by the light is proportional to the width of thedepletion region near the semiconductor surface. The photovoltage can bemeasured using capacitive coupling of a conductive electrode to thesurface of the sample. The advantage of this method over regular CVmethods is in the fact that it is not required to measure separatecontributions of the insulating gap capacitance or the oxide capacitancewhich makes the method less complicated and less sensitive to errors insensor positioning. However, this method is not a true non-contactmethod because it contacts the specimen with an insulating film.

In U.S. Pat. No. 5,453,703 to W. C. Goldfarb, which patent isincorporated herein by reference, a method and apparatus are disclosedfor determining the minority carrier surface recombination lifetimeconstant (t_(s)) of a specimen of semiconductor material. The specimenis positioned between a pair of electrodes, the specimen being disposedon one of the electrodes and being spaced from the other electrode. Asignal is provided corresponding to the capacitance between the specimenand electrode spaced from the specimen. A region of the surface of thespecimen is illuminated with a beam of light of predeterminedwavelengths and which is intensity modulated at a predeterminedfrequency and varying in intensity over a predetermined range. A fixedbias voltage V_(g) applied between the pair of electrodes, the fixedbias voltage being of a value such that the semiconductor surface is ina state of depletion or inversion. A signal is provided representing theac photocurrent induced at the region of the specimen illuminated by thelight beam. The intensity of the light beam and frequency of modulationof the light beam are selected such that the ac photocurrent is nearlyproportional to the intensity of the light beam and reciprocallyproportional to the frequency of modulation of the light beam. A signalis provided corresponding to the illumination intensity of the beam oflight. The surface minority carrier recombination time constant (t_(s))is then determined using the ac photocurrent capacitance andillumination intensity information.

In a book entitled Semiconductor Material and Device Characterization,by Dieter K. Schroder, John Wiley & Sons, Inc. 1990, p. 46, there isdisclosed a dopant measurement method for MOS capacitors using a deepdepletion condition.

It is an object of this invention to provide a new and improved methodand apparatus for characterizing a semiconductor.

It is another object of this invention to provide a new and improvedmethod and apparatus for determining the doping concentration profileand average doping concentration of a specimen of semiconductormaterial.

It is another object of this invention to provide a non-contact methodand apparatus for determining the doping concentration profile andaverage doping concentration of a specimen of semiconductor material.

It is still another object of this invention to provide a non-contactmethod and apparatus for determining the depletion width of a specimenof semiconductor material in which photovoltage (or photocurrent) ismeasured using capacitive coupling of a sensor electrode to the surfaceof the specimen.

It is a further object of this invention to provide a method andapparatus as described above which is particularly suitable forcharacterization of specimens with high density of slow surface states,e.g. non-passivated wafers.

It is still a further object of this invention to provide a new andimproved sensor assembly for use in non-contact measuring ofsemiconductor surface photovoltage or photocurrent.

It is another object of this invention to provide a new and improvedcapacitive pickup type sensor assembly.

It is still another object of this invention to provide a non-contactmethod of measuring semiconductor surface properties.

It is another object of this invention to provide a non-contact methodand apparatus for determining the depletion width of a semiconductor bymeasuring the capacitance of the depletion width in series with a knowncapacitance, rather than using light.

It is still another object of this invention to provide a non-contactmethod and apparatus for determining the depletion width of asemiconductor using capacitive coupling and the application of a biasvoltage which does not utilize photocurrent or photovoltage and whereinthe semiconductor is disposed on one electrode and spaced from anotherelectrode and wherein the air gap between the semiconductor and thespaced apart electrode is not fixed but rather varies according to theelectrostatic force between the two electrodes as a bias voltage isapplied.

SUMMARY OF THE INVENTION

According to one embodiment of this invention, a non-contact method isprovided for determining the doping concentration profile of a specimenof semiconductor material, the specimen having a surface arranged forillumination, the method comprising providing a pair of electrodes,positioning the specimen between the pair of electrodes, the specimenbeing disposed on one of the electrodes and spaced from the otherelectrode by a nonconducting medium, illuminating a region of thesurface of the specimen arranged for illumination with a beam of lightof wavelength shorter than that of the energy gap of the semiconductor,the beam of light being intensity modulated at a predeterminedfrequency, applying a variable DC voltage between the pair ofelectrodes, the variable DC bias voltage varying between thatcorresponding to accumulation and that corresponding to deep depletionfor the specimen, the intensity of the light beam being low enough andthe rate at which the DC bias voltage varies being fast enough such thatno inversion layer is formed at the surface of the specimen, providing asignal representing the ac photocurrent at the region of the specimenilluminated by the light beam, the intensity of the light beam andfrequency of modulation of the light beam being such that the acphotocurrent is nearly proportional to the intensity of the light beam,providing a signal corresponding to the total capacitance between thetwo electrodes during the DC bias voltage sweep, providing a signalcorresponding to the variable DC bias voltage, and then, determining thedoping concentration profile using the ac photocurrent, totalcapacitance and DC bias voltage information.

Instead of providing a signal representing the ac photocurrent, a signalmay be provided corresponding to the ac photovoltage.

Once the doping concentration profile has been determined, the averagedoping concentration can be easily determined.

The apparatus of the invention includes a non-contact sensor assemblyfor determining the ac photocurrent of a specimen of semiconductormaterial, the non-contact sensor assembly including a sensor tip whichis mounted on an air bearing assembly, the air bearing assembly beingmounted through a bellows assembly on the bottom of a housing assembly,the bellows assembly including a bellows, the air bearing assembly beingsupplied air through the bellows, the sensor tip including a coatingwhich serves as a reference electrode and a coating which serves as aguard electrode.

According to one implementation of the invention, the sensor tipincludes a soft, compliant bottom protective layer to protect the sensortip from mechanical damage that could be caused if large particles werepresent on the surface of the specimen.

According to another feature of the invention, a method and apparatusare provided for determining the resistivity and resistivity profile ofa specimen of semiconductor material.

According to a further feature of the invention, the reference electrodeis circularly shaped, the guard electrode is annularly shaped and bothelectrodes are disposed on the bottom surface of a transparentsubstrate.

According to another embodiment of this invention, a non-contact methodis provided for determining the doping concentration profile of aspecimen of semiconductor material, the method comprising providing apair of electrodes, positioning the specimen between the pair ofelectrodes, the specimen being disposed on one of said electrodes andspaced from said other electrode by a nonconducting gaseous medium,applying a variable DC bias voltage between the pair of electrodes, thevariable bias voltage varying between that corresponding to accumulationand that corresponding to depletion for the specimen, the rate at whichthe DC bias voltage varies being such that no inversion layer is formedat the surface of the specimen and the period of variation being smallcompared to the amount of time required to charge or discharge thesurface states associated with an unknown surface, providing a signalcorresponding to the DC bias voltage, providing a signal correspondingto the total capacitance between the two electrodes during the DC biasvoltage sweep, providing information corresponding to the area of theelectrode spaced from the specimen, determining the capacitance of thenonconductive gaseous medium using the total capacitance signal,determining the depletion width using the total capacitance, thecapacitance of the nonconducting gaseous medium and the area of theelectrode spaced from the specimen information, and determining thedoping concentration profile using the depletion width, the totalcapacitance, the DC bias voltage, and the area of the electrode spacedfrom the specimen information.

In another embodiment of the invention photovoltage or photocurrent isnot measured, the specimen is biased into accumulation and a correctionis applied to the charge on the sensor electrode to compensate forchanges in the air gap between the sensor electrode and thesemiconductor as the bias voltage is applied.

In still another embodiment of the invention, it is not necessary thataccumulation be reached and it is immaterial whether an inversion layeris present. In this embodiment the capacitance of the nonconductivegaseous medium is determined by applying high intensity light to thespecimen. In an implementation of this embodiment of the invention, thesensor assembly includes a high intensity light source.

Various features and advantages will appear from the description tofollow. In the description, reference is made to the accompanyingdrawings which form a part thereof, and in which is shown by way ofillustration, a specific embodiment of an apparatus for practicing theinvention. This embodiment will be described in sufficient detail toenable those skilled in the art to practice the invention, and it is tobe understood that other embodiments may be utilized and that structuralchanges may be made without departing from the scope of the invention.The following detailed description is therefore, not to be taken in alimiting sense, and the scope of the present invention is best definedby the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings wherein like reference numerals represent like parts:

FIG. 1 is a schematic block diagram of an apparatus for practicing theinvention; FIG. 2 is a more detailed view of the sensor assembly shownin FIG. 1;

FIG. 3 is an enlarged fragmentary view of the bottom of the sensorassembly shown in FIG. 2;

FIG. 4 is a section view of the air bearing mounting cell shown in FIG.3;

FIG. 5 is a top plan view of the air bearing mounting cell shown in FIG.3;

FIG. 6 is a perspective view of the sensor tip shown in FIG. 2;

FIG. 7 is an enlarged front section view of the sensor tip shown in FIG.2;

FIG. 8 is a section view taken along lines 8-8 in FIG. 7;

FIG. 9 is a section view taken along lines 9-9 in FIG. 7;

FIG. 10 is a section view taken along lines 10-10 in FIG. 7;

FIG. 11 is a right side view of the sensor tip shown in FIG. 7;

FIG. 12 is a graph showing how the sensor voltage and guard voltage varyin time as measurements of doping concentration are being made accordingto this invention;

FIG. 13 is a schematic block diagram of another embodiment of theinvention; and

FIG. 14 is a fragmentary view of the sensor assembly shown in FIG. 13.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present invention is directed to a method and apparatus fordetermining the doping concentration profile of a specimen ofsemiconductor material. In one embodiment, a method and apparatus usingan intensity modulated beam of light and a variable DC bias voltage isdescribed wherein the modulated light level is low enough and thevariable DC bias voltage changes fast enough so that no inversion layeris formed at the specimen surface, i.e. the specimen reaches anon-equilibrium state of deep depletion. The present invention is alsodirected to a non contact, capacitive pickup type sensor assembly formaking surface photovoltage measurements of a specimen of semiconductormaterial. In other embodiments an intensity modulated beam of light isnot utilized.

As will hereinafter become apparent, the doping concentration profileaccording to this invention can be determined using a capacitive pickuptype sensor assembly of other than as described herein. Also, thecapacitive pickup type sensor assembly of certain embodiments of thisinvention can be used for making surface photovoltage (or photocurrent)measurements for purposes other than determining doping concentrationand for making measurements other than surface photovoltage (orphotocurrent) and can be used for determining doping concentrationwithout making surface photovoltage (or photocurrent) measurements.

Referring now to the drawings, there is shown in FIG. 1 a simplifiedblock diagram of an apparatus for determining parameters such as thedoping concentration profile of a specimen of semiconductor materialaccording to this invention. Portions of the apparatus not pertinent tothis invention are not shown. In the illustration, the specimen ofsemiconductor material is identified by reference numeral 11 and theapparatus of this invention is identified by reference numeral 13.

Specimen 11 has two major surfaces 15 and 17, respectively, surface 15being the surface under testing. Specimen 11 may comprise a sample withhigh density of slow surface states, e.g. non passivated wafers andepitaxially grown films.

Apparatus 13 includes a back electrode 19 and a non contact capacitivepickup type sensor assembly 21. Back electrode 19 is constructed in theform of a wafer chuck and, as such, in addition to functioning as anelectrode serves to support and hold specimen 11 fixed during testing.Back electrode 19 is made of a conductive metal, such as aluminum.Specimen 11 is mounted on back electrode 19 with surface 15 facingupward and surface 17 in contact with or closely spaced from backelectrode 19 facing downward. Back electrode 19 is fixedly mounted on awafer positioner 20 which is movable in R and theta directions so thatdifferent parts of the surface of specimen 11 on back electrode 19 canbe positioned under sensor assembly 21 for testing.

Sensor assembly 21 is fixedly mounted vertically with respect tospecimen 11.

Sensor assembly 21 which is shown in more detail in FIG. 2 and furtherenlarged and in a fragmentary view in FIG. 3 includes a sensor tip 22.

Sensor tip 22 which is also shown in FIGS. 6 through 11 includes atruncated pyramid shaped transparent substrate 23, which may be forexample quartz, the front and rear faces of substrate 23 being verticaland the side faces 24-3 and 24-4 being slanted. If desired, the frontand rear faces could also be slanted, or all four faces made vertical. Apair of opaque conductive coatings 24-1 and 24-2, which may be forexample titanium tungsten, are formed on substrate 23 along with atransparent insulative coating 25, such as silicon oxide. A pair ofcoatings 27 and 29 of conductive transparent material are formed oninsulative coating 25. Coating 27 is circular in shape and serves as areference or sensor electrode. Coating 23 is annularly shaped and servesas a guard electrode. Both coatings 27 and 29 may be made of indium-tinoxide the thickness of which determines its transparency. The thicknessof coating 27 and its composition are such that it is transparent.Reference electrode 27 is smaller than specimen 11. Coating 29 ispreferably, nontransparent; however, it is not essential that it benontransparent. A soft protective transparent layer 30 which may be aplastic such as polyamide is formed underneath insulative coating 25 andelectrodes 27 and 29. Coating 24-1 is electrically connected toreference electrode 27 by a quantity of conductive material 32-1disposed in a first window 33 formed in insulative coating 25 and aquantity of conductive material 33-1 disposed in a second window 33-2formed in coating 25. Layer 24-2 is electrically connected to guardelectrode 29 by a quantity of conductive material 35 disposed in awindow 37 formed in insulative coating 25 and at the other end toconductor 32-4. Conductive material 32-1 and 32-3 may be, for exampleindium-tin-oxide.

Referring to FIG. 2, sensor assembly 21 further includes an illuminationassembly 39, a condenser lens assembly 41, a housing assembly 43, abellows assembly 45, an air bearing assembly 47, a field lens assembly48 and a guard sleeve 49.

Illumination assembly 39 includes a light source 51 in the form of anLED, an adjusting plate 53 and a mount 55. Adjusting plate 53 is mountedon mount 55 by screws (not shown) such that it can be adjusted in theX-Y direction relative to mount 55 and then fixedly mounted to mount 55by tightening said screws.

Condenser lens assembly 41 includes a lens mount 57 and a condenser lens59. Condenser lens 59 is fixedly mounted on lens mount 57. Lens mount 51includes a field stop 60.

Housing assembly 43 includes a housing 61 which is shaped to include apair of air inlet ports 61-1 and 61-2. A 50/50 beamsplitter 63, anincident light photodiode 65, a reflected light photodiode 67, anincident light photodiode printed circuit board 69, a reflected lightphotodiode printed circuit board 71 and an objective lens cell assembly73 having an objective lens 75 mounted in an objective lens holder 77are all mounted inside housing 61.

Bellows assembly 45 includes an annular shaped upper mounting plate 79,outer and inner bellows 81 and 83, respectively, an annular shaped lowermounting plate 85 and a bellows assembly screw 86. Bellows 81 and 83 areattached at their upper ends 81-1 and 83-1 to upper mounting plate 79and at their to lower ends 81-2 and 83-2 to mounting plate 85. Uppermounting plate 79 is fixedly mounted on the bottom of housing 61.Bellows 83 is disposed inside bellows 81. Bellows assembly screw 86 hasan axial bore 86-1 for light transmission and is used to secure bellows83 to upper mounting plate 79.

Air bearing assembly 47 includes an air bearing housing 87, a ring 89 ofporous ceramic material fixedly mounted by adhesive (not shown) inhousing 87 and a mounting cell 91 having orifices 93-1 through 93-8.Orifices 93-3 through 93-8 are for passage of air and orifices 93-1 and93-2 are for passage of conductors 32-2 and 32-4. Air bearing housing 87is secured to the bottom of lower mounting plate 85 by a Delrin nut 92.Sensor tip 22 is fixedly mounted with respect to air bearing housing 87so that it extends out of the bottom surface 94 of bearing housing 87and positioned so that it is underneath field lens 95 and about 0.5micron above the specimen when in use.

Guard sleeve 49 is mounted on upper mounting plate 79 and serves toprotect bellows assembly 45 and air bearing assembly 47.

Field lens assembly 48 includes a field lens 95 and a field lens mount97.

Lead 32-2 extends up passage ways 93-4 and 93-5 to connector 93-3. Lead32-3 (not shown) connects in a similar manner between connector 93-3 and93-6. Lead 32-5 (not shown) connects between connector 93-6 and printedcircuit board 69 where connection is made to lead 98-2 in FIG. 1.Connections are made between coating 29 and lead 98-1 of FIG. 1 in asimilar manner.

Apparatus 13 further includes a capacitance test signal source 99, anoscillator 101, a light controller and modulator 103, a referenceelectrode bias voltage source 105, a guard electrode bias voltage source107, a signal amplifier 109, a demodulator 111, a data acquisitionsystem 113, a pair of high pressure air supplies 114 and 115 and acomputer 116.

Capacitance test signal source 99 provides a small (i.e. a few tens ofmillivolts) ac potential signal on back electrode 19 so that thecapacitance between wafer 11 and sensor electrode 27 can be measured.Oscillator 101 provides signals to drive LED 51 and capacitance testsignal source 99. Also, oscillator 101 provides a synchronizing signalto light controller and modulator 103 and demodulator 111. Lightcontroller and modulator 103, ac modulates and varies the amplitude ofthe signal provided from oscillator 101 to LED 51 so as to produce an acmodulated light beam of suitable intensity.

Reference electrode bias voltage source 105 produces a variable dcvoltage whose sweep rate is controlled by computer 116. Guard electrodebias voltage source 107 produces a variable DC voltage sufficient toplace an area of the surface of specimen 11 surrounding an areacontrolled by reference electrode 27 in accumulation during the timewhen the area of specimen 11 controlled reference electrode 27 ischanged from accumulation to depletion.

Signal amplifier 109 amplifies the signal received from referenceelectrode 27. Demodulator 111, which is a synchronous demodulator,changes the ac signals received from signal amplifier 109 to dc signals.Data acquisition system 113 converts analog signals received fromvoltage sources 105 and 107, demodulator 111 and light controller andmodulator 103 into digital signals and converts digital signals fromcomputer 116 into analog signals. Computer 116 controls the overalloperations of system 13 and processes test information received. Voltagesources 105 and 107 are connected to reference and guard electrodes 27and 29, respectively, through separation resistors 117 and 119respectively. Signal amplifier 109 is connected to line 31 by isolationcapacitor 121.

Air supplies 114 and 115 are controlled by computer 116 and areconnected to ports 61-1 and 61-2, respectively.

In using apparatus 13, specimen 11 is placed on back electrode 19 afterremoving back electrode 19 from under sensor assembly 21 using waferpositioner 20. Specimen 11 is then positioned under sensor assembly 21using wafer positioner 20. Initially, air bearing assembly 47 (andsensor tip 22 which is mounted thereon) is suspended against gravity byinner and outer bellows 83 and 81 respectively, at a point approximately2 mm above specimen 11. Bellows 83 and 81 act like extension springs,exerting an upward force on air bearing assembly 47 proportional to thedistance extended. Air is then directed into housing 43 through pressureports 61-1 and 61-2 to control the vertical position (along the Z axis)of air bearing assembly 47 (and sensor tip 22 which is mounted thereon)with respect to specimen 11. Position control of air bearing assembly isaccomplished in three phases: I) coarse approach and leveling; II)near-contact approach; and III) departure.

Coarse Approach and Leveling Phase

Air, at a pressure of approximately 40 PSIG, is first admitted topressure port 61-1. The air is prevented from leaking upwards by lens 75and lens cell 77, but it is conducted downward by orifice 86-1 in screw86 into the interior space 83-3 of inner bellows 83. The pressure of theair in space 83-3 applies a downward force against sensor cell 91-1 andalso causes flow down and out through orifices 93-1 through 93-6. Saidforce causes air bearing assembly 47 to move part-way down towardspecimen 11. Additionally, air, at a pressure of approximately 8 PSIG,is admitted to pressure port 61-2 and is conducted by ports 61-3 and79-1 into the annular space 81-1 which exists between outer bellows 81and inner bellows 83. The pressure of the air in space 81-1 applies adownward force against end cap 85, causing air bearing assembly 47 tomove farther toward specimen 11, and acting in opposition to the tensionforce developed by the extension of bellows 83 and 81. As air bearingassembly 47 approaches within 20-40 micrometers of specimen 11, the airflowing out through orifices 93-1 through 93-6 creates pressurized airfilm 47-1, opposing further downward motion of air bearing assembly 47and creating a condition of force equilibrium such that air bearingassembly 47 floats at a stable height of approximately 20 micrometersabove specimen 11. The presence of multiple identical orifices 93-1through 93-6 ensures that air bearing assembly 47 floats parallel tospecimen 11, even if air bearing assembly 47 was not perfectly parallelto specimen 11 at the initial 2 mm height. The pressure of the air inspace 81-1 also forces flow through port 94 and thence through porousring 89; however, the porosity of said porous ring is so low that saidflow is negligible compared to the flow previously mentioned out oforifices 93-1 through 93-6.

At the conclusion of this approach and leveling phase, the gap betweenair bearing assembly 47 and specimen 11 is approximately 20 micrometers,and positioner 20 may be exercised to adjust the horizontal (X-Y)position of specimen 11 with respect to sensor tip 22.

Near-Contact Approach Phase

After equilibrium has been achieved in the coarse approach and levelingphase, the pressure of the air admitted to pressure port 61-2 isincreased to approximately 25 PSIG. The increased pressure of the air inspace 81-1 applies additional downward force against endcap 85, causingair bearing assembly 47 to descend further toward specimen 11. Saidincreased pressure also causes increased flow through porous right 89,which increases the pressure in air film 47-1 as said air filmapproaches 2-4 micrometers in thickness. Then the pressure of the airadmitted to pressure port 61-1 is decreased to approximately atmosphericpressure. As the flow through orifices 93-1 through 93-6 subsides, airbearing assembly 47 descends to a final height of approximately 2micrometers above specimen 11, supported on air film 47-1, which is nowmaintained by the flow through porous ring 89. The stiffness of air film47-1 under said conditions is sufficient to maintain the 2 micrometerheight of air bearing 47 above specimen 11, even in the presence ofelectrostatic forces between sensor tip 22 and specimen 11, within plusor minus approximately 0.1 micrometer.

At the conclusion of this near-contact approach phase, the gap betweenair bearing assembly 47 and specimen 11 is approximately 2 micrometers,and measurements of specimen 11 using sensor tip 22 can be accomplished.

Departure Phase

To initiate the departure phase, the pressure of the air admitted toport 61-1 is increased to approximately 40 PSIG. As detailed above, thisresults in an outflow through orifices 93-1 through 93-6, which in turncauses the pressure in air film 47-1 to increase, thereby increasing theheight of air bearing assembly 47 above specimen 11. Then the pressureof the air admitted to pressure port 61-2 is decreased to approximately8 PSIG. The decreased pressure of the air in space 81-1 reduces thedownward force against endcap 85, causing air bearing assembly 47 torise further away from specimen 11 due to the tension in bellows 83 and81. Equilibrium is achieved when air film 47-1 is approximately 20micrometers thick. At this point, further adjustments to the horizontal(X₋₋ Y) position of specimen 11 with respect to sensor tip 22 may becarried out using positioner 20, if desired. Then the near-contactapproach phase described above may be repeated. Alternatively, hedeparture phase can continue as follows.

The pressure of the air admitted to pressure port 61-2 is decreased toatmospheric. With the resulting decreased pressure of the air in space81-1, the tension in bellows 83 and 81 pulls air bearing assembly 47further away from specimen 11. Finally, the pressure of the air admittedto pressure port 61-1 is also decreased to atmospheric, and the tensionin bellows 83 and 81 pulls air bearing assembly 47 up to its initialequilibrium position at approximately 2 mm above specimen 11. Sensorassembly 21 is then positioned above specimen 11.

As can be appreciated, air from supplies 114 and 115 serves twopurposes, namely (1) form an air bearing for sensor assembly 21 and (2)cause bellows 81 and 83 to expand in order to lower sensor assembly 21into the desired position for testing.

Light source 51, which is ac intensity modulated and controlled by lightcontroller and modulator 103 as instructed by computer 115, is focusedby lens 59 on stop 60. Light emerging from stop 60 and reflected bybeamsplitter 63 strikes photodiode 65. Light transmitted throughbeamsplitter 63 from stop 60 passes through objective lens 75, throughfield lens 95, through sensor tip 22 and strikes specimen 11 to generateac photovoltage. The light reflected from specimen 11 passes backthrough field lens 95 and objective lens 75 and is then split 50/50, sothat 50% of it is detected by photodiode 67. The signal from photodiode67 is fed by wire 122 to data acquisition subsystem 113 through anamplified signal path in signal amplifiers 109 (not shown) into PCB 71which is coupled to computer 116 by a wire (not shown). Light from stop60 that is reflected off beamsplitter 63 strikes incident lightphotodiode 65. The signal from incident light photodiode 65 is fed by awire 123 to data acquisition system 113 through an amplified signal pathin signal amplifiers 109. The difference in intensity of the lightstriking specimen 11, which is the same with suitable anti-reflectivecoatings applied to air-dielectric interfaces. The difference inintensity of the light striking specimen 11, which is the same withsuitable anti-reflective coatings applied to air-dielectric interfacesas the intensity of the light from stop 60 that is reflected offbeamsplitter 63 into photodiode 65 since beamsplitter 63 splits in halfthe light from stop 60, and the light reflected from specimen 11 isequal to the light absorbed by specimen 11 (i.e. absorbed flux is equalto incident flux minus reflected flux). With specimen 11 so illuminatedand absorbed flux so measured time-varying bias voltages from sources105 and 107, controlled by computer 51, are applied to their respectiveelectrodes 27 and 29 through separation resistors 117 and 119,respectively.

The ac photovoltage signal developed on the surface 15 of specimen 11upon illumination, which is of one frequency, and the ac capacitancetest signal from source 99 which is of a frequency different from the acphotovoltage signals are capacitively picked up simultaneously byreference electrode 27 and fed through an isolation capacitor 121 intosignal amplifier 109 where they are separated into different channelsusing conventional electrical filter circuits. Signals picked up byguard electrode 29 are shunted to ground. As can be appreciated, guardelectrode 29 also serves to avoid fringing field problems in theapplication of the bias field by the reference electrode and also servesto limit the area on surface 15 of specimen 11 that provides the acsurface photovoltage signal to reference electrode 27. The output ofsignal amplifier 109 is fed into demodulator 111. The output ofdemodulator 111 is fed into data acquisition system 113 whose output isfed into computer 115.

A method of determining the doping concentration profile N_(sc) (Z)according to this invention and using apparatus 13 will now bedescribed.

The first step involves determining the value of the induced chargeQ_(ind) at a plurality of points in time during the measurement segmentof the sweep period, the measurement segment being the time period whenthe voltage applied to reference electrode 27 varies from thatcorresponding to accumulation to that corresponding to deep depletion asshown in FIG. 12. The induced charge Q_(ind) is determined using theformula:

    Q.sub.ind =C.sub.tot ·V.sub.p

where:

C_(tot) =total capacitance between the pair of electrodes 19 and 27, and

V_(p) =sensor potential (i.e. the bias voltage applied betweenelectrodes 19 and 27).

Then, Wd is determined for the same plurality of points in time usingthe formula:

    I.sub.ac =|e|/ε.sub.si ·C.sub.tot ·W.sub.d ·φ,

where:

W_(d) =the depletion layer width,

e=electron charge,

ε_(si) =dielectric constant of Si,

C_(tot) =total capacitance between the pair of electrodes,

φ=absorbed flux (photons/cm² ·s) where s=seconds and

I_(ac) =current induced in the reference electrode by the ac surfacephotovoltage.

Then, the doping concentration profile is determined using the formula:

    N.sub.sc (Z)=(-1/eA)·(dQ.sub.ind /dW.sub.d)

where:

N_(sc) (Z) the doping concentration at a depth Z,

A=the sensor area, and

Z=W_(d)

Once N_(sc) (Z) has been determined, the resistivity can be determinedusing well known computations. For example, for boron-doped silicon theresistivity can be determined using a commonly accepted formula such as:

    ρ=(6.242×10.sup.13 /N.sub.sc)·10.sup.t

where:

    t=(A.sub.0 +A.sub.1 ·Y+A.sub.2 ·Y.sup.2 +A.sub.3 ·Y.sup.3)/(1+B.sub.1 ·Y+B.sub.2 ·Y.sup.2 +B.sub.3 ·Y.sup.3)

where:

y=(log₁₀ N_(sc))-16,

A₀ =-3.0769,

A₁ =2.2108,

A₂ =-0.62272,

A₃ =0.057501,

B₁ =-0.68157,

B₂ =0.19833, and

B₃ =-0.018376

Referring now to FIG. 12 there is shown a graph of an example how thebias voltage applied to reference electrode 27 and guard electrode 29may vary for the following conditions, the conditions being selected forillustrative purposes only:

LED (light source) modulation frequency 100 kHz;

Bias sweep period 10 ms;

Maximum bias voltage 200V;

Incident flux 10¹³ photons/cm² /s.

Instead of air, another nonconductive gas could be used such as drynitrogen. Similarly, a non-conducting, non-gaseous medium, such asmylar, could be used in an implementation of the invention whichcontacts the wafer.

In a situation where the amount of optically generated minority carriers(optically injected charge) is small enough not to create an inversionlayer, but not small enough negligible compared to the charge in thedepletion region, the following method can be used to correct for theoptically injected charge.

    Q.sub.ind =-(Q.sub.sc +Q.sub.inj)                          (1)

    Q.sub.ind =C.sub.tot ·V.sub.probe,                (2)

    Q.sub.sc =eA∫N.sub.sc (Z)dz,                          (3)

    Q.sub.inj =eA . φ. t,                                  (4)

where φ is the optical flux and t is time from the start of thedepletion part of the sweep.

Q_(ind) and Q_(inj) are found from measurements and equations (2) and(4); Q_(sc) is found from (1), and then the doping profile N_(sc) (Z) isfound from (3).

Instead of using photovoltage (or photocurrent), the depletion width canbe measured according to another embodiment of this invention bymeasuring the capacitance of the depletion width and then calculatingthe depletion width from the capacitance. The method is as follows:

a. providing a pair of electrodes,

b. positioning the specimen between the pair of electrodes, the specimenbeing disposed on one of said electrodes and spaced from said otherelectrode by a nonconducting gaseous medium,

c. applying a variable DC bias voltage between the pair of electrodes,the variable bias voltage varying between that corresponding toaccumulation and that corresponding to depletion for the specimen,

d. the rate at which the DC bias voltage varies being such that noinversion layer is formed at the surface of the specimen and the periodof variation being small compared to the amount of time required tocharge or discharge the surface states associated with an unknownsurface,

e. providing a signal corresponding to the DC bias voltage,

f. providing a signal corresponding to the total capacitance between thetwo electrodes during the DC bias voltage sweep,

g. providing information corresponding to the area of the electrodespaced from the specimen,

h. determining the capacitance of the nonconductive gaseous medium usingthe total capacitance signal,

i. determining the depletion width using the total capacitance, thecapacitance of the nonconducting gaseous medium and the area of theelectrode spaced from the specimen information, and

j. determining the doping concentration profile using the depletionwidth, the total capacitance, the DC bias voltage, and the area of theelectrode spaced from the specimen information, wherein determining thecapacitance of the nonconductive gaseous medium comprises measuring thetotal capacitance between the two electrodes when the DC bias voltagecorresponds to that for accumulation for the specimen and wherein thedepletion width is determined using the formula

    W.sub.d =ε.sub.s ε.sub.o A[(1/C.sub.tot)-(1/C.sub.ngm)]

where:

W_(d) =the depletion layer width,

ε_(s) =the relative dielectric constant of the semiconductor,

ε_(o) =the absolute dielectric constant of a vacuum,

A=the area of the electrode spaced from the specimen,

C_(tot) =the total capacitance between the pair of electrodes, and

C_(ngm) =the capacitance of the nonconducting gaseous medium,

where: ##EQU1## where: C_(sc) =the capacitance of the space changeregion.

Once the depletion width is determined, the doping concentration profileis determined using the formula

    N(W.sub.d)=C.sup.3.sub.tot /qε.sub.s ε.sub.o A.sup.2 (dC.sub.tot /dV)

where:

N=the doping concentration,

W=the depletion layer width,

C_(tot) =the total capacitance between the pair of electrodes

q=the elementary charge

ε_(s) =the relative dielectric constant of the specimen,

ε_(o) =the absolute dielectric constant of a vacuum,

A=the area of the electrode spaced from the specimen, and

V=the applied DC bias voltage.

The apparatus used in determining doping concentration by measuring thecapacitance of the depletion width as described above (rather than usingphotocurrent or photovoltage) can be achieved using apparatus 13 asshown in FIG. 1 with light source 51 not being energized. Also, anon-contact sensor assembly other than the air-bearing arrangement shownby FIG. 2 could also be employed in either embodiment of the method ofthis invention.

In the method described above, which does not utilize photocurrent orphotovoltage, it is assumed that the air gap is held fixed. Inactuality, the air gap is not fixed but, rather, varies according to theelectrostatic force between the electrodes as the bias voltage isapplied. Because this electrostatic force is proportional to the squareof the charge Q_(ind) on the sensor, the variation in C_(ngm) can bedescribed by the formula:

    C.sup.-1.sub.ngm (Q.sub.ind)=C.sup.-1.sub.ngm (0)+αQ.sup.2.sub.ind

where α is a constant to be determined and C_(ngm) (0) is the gapcapacitance in the absence of any electrostatic force.

Two ways are hereinafter described for determining the correction to beapplied to compensate for this change in electrostatic force.

The first way requires that the wafer be biased into accumulation whereC_(tot) =C_(ngm). After calculating the corresponding Q values from theC_(tot) and V_(bias) data, the coefficient α and C_(ngm) (0) are foundby fitting C⁻¹ _(ngm) (0)+αQ² _(ind) to the C⁻¹ _(tot) vs. Q_(ind) datafrom the accumulation part of the sweep.

A method for determining the doping concentration using the first waynoted above for correcting for changes in the air gap is as follows:

A method of determining the doping concentration profile of a specimenof semiconductor material, the method comprising:

a. providing a pair of electrodes,

b. positioning the specimen between the pair of electrodes, the specimenbeing disposed on one of said electrodes and spaced from said otherelectrode by a nonconducting medium,

c. applying a variable DC bias voltage between the pair of electrodes,the variable bias voltage varying between that corresponding toaccumulation and that corresponding to depletion for the specimen,

d. the rate at which the DC bias voltage varies being such that anyinversion layer formed at the surface of the specimen is kept to aminimum and the period of variation being small compared to the amountof time required to charge or discharge the surface states associatedwith an unknown surface,

e. providing a signal corresponding to the DC bias voltage,

f. providing a signal corresponding to the total measured capacitanceC_(tot) between the two electrodes during the DC bias voltage sweep,

g. providing information corresponding to the area of the electrodespaced from the specimen,

h. determining the capacitance of the nonconductive medium using thetotal measured capacitance in accumulation in the following manner:

i. calculating the corresponding Q_(ind) values for the measured C_(tot)vs V_(bias) data,

ii. fitting the function C⁻¹ _(ngm) (0)+αQ² _(ind) to the C⁻¹ _(tot) vsQ_(ind) data points from accumulation to obtain α and C⁻¹ _(ngm) (0)

iii. determining

    C'.sup.-1.sub.tot =C.sup.-1.sub.tot -αQ.sub.ind.sup.2

where:

C_(tot) =total measured capacitance, and

C'_(tot) =corrected total capacitance

j. determining the depletion width using the total correctedcapacitance, the capacitance of the nonconducting medium C_(ngm) (0) andthe area of the electrode spaced from the specimen information, and

k. determining the doping concentration profile using the depletionwidth, the total corrected capacitance, the DC bias voltage, and thearea of the electrode spaced from the specimen information,

l. determining the doping concentration profile using the depletionwidth, the total capacitance, the DC bias voltage, and the area of theelectrode spaced from the specimen information;

wherein the depletion width is determined using the formula:

    W.sub.d =ε.sub.s ε.sub.o A[(1/C'.sub.tot)-(1/C.sub.ngm 0)]

C_(tot) =the total measured capacitance,

W_(d) =the depletion layer width,

ε_(s) =the relative dielectric constant of the semiconductor,

ε_(o) =the absolute dielectric constant of a vacuum,

A=the area of the electrode spaced from the specimen,

C'_(tot) =the total corrected measured capacitance between the pair ofelectrodes, and

C_(ngm) (0)=the capacitance of the nonconducting medium in absence ofany electrostatic force, and using the formula:

    N(W.sub.d)=C'.sup.3.sub.tot /qε.sub.s ε.sub.o A.sup.2 (dC'.sub.tot /dV)

where:

N=the doping concentration,

W=the depletion layer width,

C'_(tot) =the total corrected capacitance between the pair ofelectrodes,

q=the elementary charge

ε_(s) =the relative dielectric constant of the specimen,

ε_(o) =the absolute dielectric constant of a vacuum,

A=the area of the electrode spaced from the specimen, and

V=the applied DC bias voltage.

The second way for determining the correction to be applied tocompensate for changes in the air gap involves applying high intensitylight to the specimen, the intensity and wavelength of the light chosenbeing such as to generate an amount of free carriers in thesemiconductor sufficient to collapse any depletion regardless of appliedbias voltage. Under these conditions (as in accumulation) C_(tot)=C_(ngm), and the C_(ngm) vs. Q_(ind) data describing the gapvariationbe be readily acquired by sweeping the bias voltage. Again thecoefficient α and C_(ngm) (0) are found by fitting C⁻¹ _(ngm) (0)+αQ²_(ind) to the C_(tot) vs. Q_(ind) data. This second way eliminates theneed to bias the wafer into accumulation and is therefore more flexible.

After determining C_(ngm) (0) and α the measured C_(tot) values arecorrected by aplying

    C'.sup.-1.sub.tot =C.sup.-1.sub.tot -αQ.sup.2.sub.ind

Where C'_(tot) are the corrected values for C_(tot) and C'_(ngm)=C_(ngm) (0).

A method for determining the doping concentration using the second waynoted above for correcting for changes in the air gap is as follows:

A method of determining the doping concentration profile of a specimenof semiconductor material, the method comprising:

a. providing a pair of electrodes,

b. positioning the specimen between the pair of electrodes, the specimenbeing disposed on one of said electrodes and spaced from said otherelectrode by a nonconducting medium,

c. applying a variable DC bias voltage between the pair of electrodes,the variable bias voltage varying between that corresponding toaccumulation and that corresponding to depletion for the specimen,

d. the rate at which the DC bias voltage varies being such that anyinversion layer formed at the surface of the specimen is kept to aminimum and the period of variation being small compared to the amountof time required to charge or discharge the surface states associatedwith an unknown surface,

e. providing a signal corresponding to the DC bias voltage,

f. providing a signal corresponding to the total measured capacitancebetween the two electrodes during the DC bias voltage sweep,

g. providing information corresponding to the area of the electrodespaced from the specimen,

h. determining the capacitance of the nonconductive medium using thetotal measured capacitance C_(tot) in the following manner:

i. illuminating the specimen with a high intensity beam of light, theintensity and wavelength of the light being such that an amount of freecarriers are generated in the semiconductor sufficient to collapse anydepletion regardless of the applied bias voltage,

ii. providing a signal corresponding to the total measured capacitanceC_(tot),

iii. calculating the corresponding Q_(ind) values from the measuredC_(tot) vs V_(bias) data,

iv. fitting the function C⁻¹ _(ngm) (0)+αQ² _(ind) to the C⁻¹ _(tot) vsQ_(ind) data points to obtain α and C⁻¹ _(ngm) (0),

v. determining C'_(tot) using the formula:

    C'.sup.-1.sub.tot =C.sup.-1.sub.tot -αQ.sup.2.sub.ind

j. determining the depletion width using the total correctedcapacitance, the capacitance of the nonconducting medium C_(ngm) (0) andthe area of the electrode spaced from the specimen information, and

k. determining the doping concentration profile using the depletionwidth, the total corrected capacitance, the DC bias voltage, and thearea of the electrode spaced form the specimen information,

    W.sub.d =ε.sub.s ε.sub.o A[(1/C'.sub.tot)-(1/C.sub.ngm 0)]

where:

W_(d) =the depletion layer width,

ε_(s) =the relative dielectric constant of the semiconductor,

ε_(o) =the absolute dielectric constant of a vacuum,

A=the area of the electrode spaced from the specimen,

C'_(tot) =the total corrected measured capacitance between the pair ofelectrodes, and

C_(ngm) (0)=the capacitance of the nonconducting medium in absence ofany electrostatic force.

    N(W.sub.d)=C'.sup.3.sub.tot /qε.sub.s ε.sub.o A.sup.2 (dC'.sub.tot /dV)

where:

N=the doping concentration,

q=the elementary charge

ε_(s) =the relative dielectric constant of the specimen,

ε_(o) =the absolute dielectric constant of a vacuum,

A=the area of the electrode spaced from the specimen, and

V=the applied DC bias voltage.

Referring now to FIG. 13 there is shown a schematic block diagram ofanother embodiment of an apparatus for practicing the invention.Apparatus 13¹ differs from apparatus 13 only in the details of probeassembly 21¹. Probe assembly 21¹ shown in FIG. 14 differs from probeassembly 21 in that beamsplitter 63 and photodiodes 65 and 67, areeliminated and illumination assembly 39 is replaced by illuminationassembly 39¹. Illumination assembly 39¹ includes a high intensity lightsource 51¹ in the form of a laser diode rather than a light source 51 inthe form of an LED as in illumination assembly 39.

The embodiments of the present invention are intended to be merelyexemplary and those skilled in the art shall be able to make numerousvariations and modifications to it without departing from the spirit ofthe present invention. All such variations and modifications areintended to be within the scope of the present invention as defined inthe appended claims.

What is claimed is:
 1. A method of determining the doping concentrationprofile of a specimen of semiconductor material, the methodcomprising:a. providing a pair of electrodes, b. positioning thespecimen between the pair of electrodes, the specimen being disposed onone of said electrodes and spaced from said other electrode by anonconducting medium, c. applying a variable DC bias voltage between thepair of electrodes, the variable bias voltage varying between thatcorresponding to accumulation and that corresponding to depletion forthe specimen, d. the rate at which the DC bias voltage varies being suchthat any inversion layer formed at the surface of the specimen is keptto a minimum and the period of variation being small compared to theamount of time required to charge or discharge the surface statesassociated with an unknown surface, e. providing a signal correspondingto the DC bias voltage, f. providing a signal corresponding to the totalcapacitance between the two electrodes during the DC bias voltage sweep,g. providing information corresponding to the area of the electrodespaced from the specimen, h. determining the capacitance of thenonconductive medium using the total capacitance signal, i. determiningthe depletion width using the total capacitance, the capacitance of thenonconducting medium and the area of the electrode spaced from thespecimen information, and j. determining the doping concentrationprofile using the depletion width, the total capacitance, the DC biasvoltage, and the area of the electrode spaced from the specimeninformation.
 2. The method of claim 1, wherein the capacitance of thenonconductive gaseous medium is assumed to be constant and determiningthe capacitance of the gaseous medium comprises measuring the totalcapacitance between the two electrodes when the DC bias voltagecorresponds to that for accumulation for the specimen.
 3. The method ofclaim 1 wherein the depletion width is determined using the formula:

    W.sub.d =ε.sub.s ε.sub.o A[(1/C.sub.tot)-(1/C.sub.ngm)]

where: W_(d) =the depletion layer width, ε_(s) =the relative dielectricconstant of the semiconductor, ε_(o) =the absolute dielectric constantof a vacuum, A=the area of the electrode spaced from the specimen,C_(tot) =the total measured capacitance between the pair of electrodes,and C_(ngm) =the capacitance of the nonconducting medium.
 4. The methodof claim 3 wherein the doping concentration profile is determined usingthe formula:

    N(W.sub.d)=C.sup.3.sub.tot /qε.sub.s ε.sub.o A.sup.2 (dC.sub.tot /dV)

where: N=the doping concentration, W=the depletion layer width, C_(tot)=the total capacitance between the pair of electrodes, q=the elementarycharge ε_(s) =the relative dielectric constant of the specimen, ε_(o)=the absolute dielectric constant of a vacuum, A=the area of theelectrode spaced from the specimen, and V=the applied DC bias voltage.5. The method of claim 1, wherein the nonconductive medium is air.
 6. Amethod of determining the doping concentration profile of a specimen ofsemiconductor material, the method comprising:a. providing a pair ofelectrodes, b. positioning the specimen between the pair of electrodes,the specimen being disposed on one of said electrodes and spaced fromsaid other electrode by a nonconducting medium, c. applying a variableDC bias voltage between the pair of electrodes, the variable biasvoltage varying between that corresponding to accumulation and thatcorresponding to depletion for the specimen, d. the rate at which the DCbias voltage varies being such that any inversion layer formed at thesurface of the specimen is kept to a minimum and the period of variationbeing small compared to the amount of time required to charge ordischarge the surface states associated with an unknown surface, e.providing a signal corresponding to the DC bias voltage, f. providing asignal corresponding to the total measured capacitance C_(tot) betweenthe two electrodes during the DC bias voltage sweep, g. providinginformation corresponding to the area of the electrode spaced from thespecimen, h. determining the capacitance of the nonconductive mediumusing the total measured capacitance in accumulation in the followingmanner:i. calculating the corresponding Q_(ind) values for the measuredC_(tot) vs V_(bias) data, ii. fitting the function C⁻¹ _(ngm) (0)+αQ⁻²_(ind) to the C⁻¹ _(tot) (0) vs Q_(ind) data points from accumulation toobtain α and C⁻¹ _(ngngm) (0), iii. determining

    C'.sup.-1.sub.tot =C.sup.-1.sub.tot -αQ.sub.ind.sup.2

where: C_(tot) =total measured capacitance, and C'_(tot) =correctedtotal capacitance i. determining the depletion width using the totalcorrected capacitance, the capacitance of the nonconducting mediumC_(ngm) (0) and the area of the electrode spaced from the specimeninformation, and j. determining the doping concentration profile usingthe depletion width, the total corrected capacitance, the DC biasvoltage, and the area of the electrode spaced from the specimeninformation, k. determining the doping concentration profile using thedepletion width, the total capacitance, the DC bias voltage, and thearea of the electrode spaced from the specimen information,wherein thedepletion width is determined using the formula:

    W.sub.d =ε.sub.s ε.sub.o A[(1/C'.sub.tot)-(1/C.sub.ngm (0)]

C_(tot) =the total measured capacitance, W_(d) =the depletion layerwidth, ε_(s) =the relative dielectric constant of the semiconductor,ε_(o) =the absolute dielectric constant of a vacuum, A=the area of theelectrode spaced from the specimen, C'_(tot) =the total correctedmeasured capacitance between the pair of electrodes, and C_(ngm) (0)=thecapacitance of the nonconducting medium in absence of any electrostaticforce, and using the formula:

    N(W.sub.d)=C'.sup.3.sub.tot /qε.sub.s ε.sub.o A.sup.2 (dC'.sub.tot /dV)

where: N=the doping concentration, W=the depletion layer width, C'_(tot)=the total capacitance between the pair of electrodes, q=the elementarycharge, ε_(s) =the relative dielectric constant of the specimen, ε_(o)=the absolute dielectric constant of a vacuum, A=the area of theelectrode spaced from the specimen, and V=the applied DC bias voltage.7. A method of determining the doping concentration profile of aspecimen of semiconductor material, the method comprising:a. providing apair of electrodes, b. positioning the specimen between the pair ofelectrodes, the specimen being disposed on one of said electrodes andspaced from said other electrode by a nonconducting medium, c. applyinga variable DC bias voltage between the pair of electrodes, the variablebias voltage varying between that corresponding to accumulation and thatcorresponding to depletion for the specimen, d. the rate at which the DCbias voltage varies being such that any inversion layer formed at thesurface of the specimen is kept to a minimum and the period of variationbeing small compared to the amount of time required to charge ordischarge the surface states associated with an unknown surface, e.providing a signal corresponding to the DC bias voltage, f. providing asignal corresponding to the total measured capacitance between the twoelectrodes during the DC bias voltage sweep, g. providing informationcorresponding to the area of the electrode spaced from the specimen, h.determining the capacitance of the nonconductive medium using the totalmeasured capacitance C_(tot) in the following manner:i. illuminating thespecimen with a high intensity beam of light, the intensity andwavelength of the light being such that an amount of free carriers aregenerated in the semiconductor sufficient to collapse any depletionregardless of the applied bias voltage, ii. providing a signalcorresponding to the total measured capacitance C_(tot), iii.calculating the corresponding Q_(ind) values from the measured C_(tot)vs V_(bias) data, iv. fitting the function C⁻¹ _(ngm) (0)+αQ² _(ind) tothe C⁻¹ _(tot) vs Q_(ind) data points to obtain α and C⁻¹ _(ngm) (0), v.determining C'_(tot) using the formula:

    C'.sup.-1.sub.tot =C.sup.-1.sub.tot -αQ.sup.2.sub.ind

j. determining the depletion width using the total correctedcapacitance, the capacitance of the nonconducting medium C_(ngm) (0) andthe area of the electrode spaced from the specimen information, and k.determining the doping concentration profile using the depletion width,the total corrected capacitance, the DC bias voltage, and the area ofthe electrode spaced form the specimen information,

    W.sub.d =ε.sub.s ε.sub.o A[(1/C'.sub.tot)-(1/C.sub.ngm (0)

where: W_(d) =the depletion layer width, ε_(s) =the relative dielectricconstant of the semiconductor, ε_(o) =the absolute dielectric constantof a vacuum, A=the area of the electrode spaced from the specimen,C'_(tot) =the total corrected measured capacitance between the pair ofelectrodes, and C_(ngm) (0)=the capacitance of the nonconducting mediumin absence of any electrostatic force,

    N(W.sub.d)=C'.sup.3.sub.tot /qε.sub.s ε.sub.o A.sup.2 (dC'.sub.tot /dV)

where: N=the doping concentration, q=the elementary charge ε_(s) =therelative dielectric constant of the specimen, ε_(o) =the absolutedielectric constant of a vacuum, A=the area of the electrode spaced fromthe specimen, and V=the applied DC bias voltage.
 8. A non-contact sensorassembly for making capacitance measurements of a specimen ofsemiconductor material comprising:a. housing having a top and a bottom,b. a bellows assembly, said bellows assembly comprising an upper plate,a lower plate and a bellows connecting the upper plate to the lowerplate, said upper plate being mounted on said bottom of said housing, c.an air bearing assembly mounted on said bottom plate of said bellowassembly, d. a sensor tip mounted on said air bering assembly, saidsensor tip including an electrode, e. said housing having an inlet forreceiving air from an air supply and directing said air into said airbearing through said bellows, and f. a high intensity light source.